The weights of cans of Ocean brand tuna are supposed to have a net weight of 6 ounces. The manufacturer tells you that the net weight is actually a Normal random variable with a mean of 5.99 ounces and a standard deviation of 0.22 ounces. Suppose that you draw a random sample of 31 cans. Part i) Using the information about the distribution of the net weight given by the manufacturer, find the probability that the mean weight of the sample is less than 5.98 ounces. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). Probability (as a proportion) Part ii) Use normal approximation to find the probability that more than 49.2% of the sampled cans are overweight (i.e. the net weight exceeds 6 ounces). O A. 0.4556 OB. 0.4986 OC. 0.5444 OD. 0.5014
The weights of cans of Ocean brand tuna are supposed to have a net weight of 6 ounces. The manufacturer tells you that the net weight is actually a Normal random variable with a mean of 5.99 ounces and a standard deviation of 0.22 ounces. Suppose that you draw a random sample of 31 cans. Part i) Using the information about the distribution of the net weight given by the manufacturer, find the probability that the mean weight of the sample is less than 5.98 ounces. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). Probability (as a proportion) Part ii) Use normal approximation to find the probability that more than 49.2% of the sampled cans are overweight (i.e. the net weight exceeds 6 ounces). O A. 0.4556 OB. 0.4986 OC. 0.5444 OD. 0.5014
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The weights of cans of Ocean brand tuna are supposed to have a net weight of 6 ounces. The manufacturer tells you that the net weight is actually a Normal random variable with a mean of 5.99 ounces and a standard deviation of 0.22 ounces. Suppose that you draw a random sample of 31 cans.
**Part i)** Using the information about the distribution of the net weight given by the manufacturer, find the probability that the mean weight of the sample is less than 5.98 ounces. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places).
Probability (as a proportion) [ ]
**Part ii)** Use normal approximation to find the probability that more than 49.2% of the sampled cans are overweight (i.e. the net weight exceeds 6 ounces).
- A. 0.4556
- B. 0.4986
- C. 0.5444
- D. 0.5014](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e0d396c-e5f5-46c2-813a-9ed0820c37ca%2F64a9ad04-270a-4766-bef8-648aa6ebe16d%2Fp0p5k2b_processed.png&w=3840&q=75)
Transcribed Image Text:The weights of cans of Ocean brand tuna are supposed to have a net weight of 6 ounces. The manufacturer tells you that the net weight is actually a Normal random variable with a mean of 5.99 ounces and a standard deviation of 0.22 ounces. Suppose that you draw a random sample of 31 cans.
**Part i)** Using the information about the distribution of the net weight given by the manufacturer, find the probability that the mean weight of the sample is less than 5.98 ounces. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places).
Probability (as a proportion) [ ]
**Part ii)** Use normal approximation to find the probability that more than 49.2% of the sampled cans are overweight (i.e. the net weight exceeds 6 ounces).
- A. 0.4556
- B. 0.4986
- C. 0.5444
- D. 0.5014
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